Sector models—A toolkit for teaching general relativity: I. Curved spaces and spacetimes

Abstract

Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary mathematics. The central idea of this introduction to general relativity is the use of so-called sector models. Sector models describe curved spaces the Regge calculus way by subdivision into blocks with euclidean geometry. This procedure is similar to the approximation of a curved surface by flat triangles. We outline a workshop for high school and undergraduate students that introduces the notion of curved space by means of sector models of black holes. We further describe the extension to sector models of curved spacetimes. The spacetime models are suitable for learners with a basic knowledge of special relativity. The teaching materials presented in this paper are available online for teaching purposes, see

General relativity in upper secondary school: Design and evaluation of an online learning environment using the model of educational reconstruction

“…Concerning their motivation and attitude towards learning GR, students confirmed our hypothesis, in line with observations of Zahn and Kraus [2]. They wanted to learn more about the nature of space and time because they perceived the topic to be modern and relevant:…”

“…Teaching GR is challenging both technically and conceptually, because of the advanced math and the large amount of previous knowledge, notably special relativity, required [2,54,55]. Learners lack experience with relativistic phenomena and the counterintuitive nature of these phenomena poses yet another difficulty [15,56].…”

“…before by education researchers and physicists [2,53,54,65]. Even though GR relies on an advanced mathematical foundation, the theory is geometric in its nature.…”

“…This analogy compares spacetime to a rubber sheet that gets distorted by massive objects. It is a popular, yet controversial way of illustrating GR [2,53,67]. We found that even though most students showed awareness of the limitations of an analogy that reduces the number of dimensions, many did not address the temporal dimension of spacetime explicitly [66].…”

“…Nonetheless, physicists and science educators argue for introducing GR in schools because of its far-reaching scientific, philosophical, and cultural importance [1][2][3]. Not only does the theory constitute our best understanding of the Universe, it continues to inspire scientific and technological progress and has become an issue of practical concern to mainstream physicists and engineers [4].…”